Line an 8x8-inch baking dish with parchment paper, making sure it extends up the sides for easy removal later. Set aside.
Add the white chocolate chips, sweetened condensed milk, butter, and a pinch of salt to a medium saucepan. Cook over low heat, stirring constantly, until the mixture is fully melted and smooth.
Take the pan off the heat and stir in the peppermint extract until evenly combined.
Pour the mixture into the prepared baking dish, spreading it out into an even layer with a spatula.
Sprinkle the crushed candy canes evenly over the top, gently pressing them in so they stick.
Place the dish in the refrigerator and chill for at least 4 hours, or until the fudge is firm.
Once set, lift the fudge out of the pan using the parchment paper. Cut into neat squares (5x5 or 6x6 rows usually give a good size for sharing).
Serve and enjoy or store in an airtight container.